Question Bank • QB_FP_042 NAT • 2 Marks

Section 3: Farm Power

Farm Power

Subtopic: I.C. engine systems – fuel, cooling, lubrication, ignition, electrical, intake and exhaust

Question Statement:

In a Common Rail Direct Injection (CRDI) tractor diesel engine, fuel is injected at a rail pressure of $P_{\text{rail}} = 160\text{ MPa}$ into a combustion chamber where the compressed air pressure is $P_{\text{cyl}} = 6\text{ MPa}$. The density of diesel fuel is $\rho_f = 840\text{ kg/m}^3$. The theoretical fuel exit velocity through the injector nozzle orifice in $\text{m/s}$ is ________ (round off to 1 decimal place).

Answer Key:

605.5

Step-by-Step Solution & Explanation

1. Effective pressure drop across nozzle orifice ($\Delta P$): $\Delta P = P_{\text{rail}} - P_{\text{cyl}} = 160 - 6 = 154\text{ MPa} = 154 \times 10^6\text{ N/m}^2$ 2. Theoretical jet exit velocity by Torricelli's Bernoulli equation: $v_{th} = \sqrt{\frac{2 \Delta P}{\rho_f}} = \sqrt{\frac{2 \times 154 \times 10^6}{840}} = \sqrt{\frac{308 \times 10^6}{840}} = \sqrt{366,666.7} \approx 605.53\text{ m/s} \approx 605.5\text{ m/s}$
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